Matlab: how can I perform row operations without brute-force for loop?

Question

I need to do function that works like this :

N1 = size(X,1);
N2 = size(Xtrain,1);
Dist = zeros(N1,N2);

    for i=1:N1
        for j=1:N2
            Dist(i,j)=D-sum(X(i,:)==Xtrain(j,:));
        end
    end

(X and Xtrain are sparse logical matrixes)

It works fine and passes the tests, but I believe it's not very optimal and well-written solution.

How can I improve that function using some built Matlab functions? I'm absolutely new to Matlab, so I don't know if there really is an opportunity to make it better somehow.

Answer 1

You wanted to learn about vectorization, here some code to study comparing different implementations of this pair-wise distance.

First we build two binary matrices as input (where each row is an instance):

m = 5;
n = 4;
p = 3;
A = double(rand(m,p) > 0.5);
B = double(rand(n,p) > 0.5);

1. double-loop over each pair of instances

D0 = zeros(m,n);
for i=1:m
    for j=1:n
        D0(i,j) = sum(A(i,:) ~= B(j,:)) / p;
    end
end

2. PDIST2

D1 = pdist2(A, B, 'hamming');

3. single-loop over each instance against all other instances

D2 = zeros(m,n);
for i=1:n
    D2(:,i) = sum(bsxfun(@ne, A, B(i,:)), 2) ./ p;
end

4. vectorized with grid indexing, all against all

D3 = zeros(m,n);
[x,y] = ndgrid(1:m,1:n);
D3(:) = sum(A(x(:),:) ~= B(y(:),:), 2) ./ p;

5. vectorized in third dimension, all against all

D4 = sum(bsxfun(@ne, A, reshape(B.',[1 p n])), 2) ./ p;
D4 = permute(D4, [1 3 2]);

Finally we compare all methods are equal

assert(isequal(D0,D1,D2,D3,D4))